REPUBLICAN WILLIAMSON EAGER FOR AN OPPONENT

The Republican who will challenge for the seat of longtime U.S. Sen. Alan Dixon eagerly watched the Democratic returns Tuesday night, anticipating his battle in November with new hope.

With Carol Mosely Braun in a tight race with Dixon Tuesday night, Williamson, a conservative former White House adviser to Presidents Bush and Reagan, was thinking of the possibility of a completely different race this fall.

Instead of facing an incumbent conservative Democrat with some similar values, Williamson could go to the polls in November against a mirror opposite: a black woman far more liberal than Dixon.

Speaking to a crowd of Republicans gathered at the Hyatt Regency Hotel, Williams said, ''One thing is clear: Democratic voters are angry, and they`re voting for fundamental change. For any that didn`t believe it before tonight, Rich Williamson is going to win in November.''

He refused to say which Democrat he would rather face, but he did say that ''whoever emerges from this primary can be and will be beaten in November.''

A former chairman of the American Conservative Union, Williamson, 42, is an architect of the new conservatism that guided the Reagan years. He has served as U.S. ambassador to United Nations offices in Europe and as an assistant secretary of state. He is a partner in the Chicago law firm of Mayer Brown & Platt.

Williamson, who has been active in conservative politics since his college years, also has worked in numerous presidential campaigns, including those of now-Housing and Urban Development Secretary Jack Kemp and former Nevada Sen. Paul Laxalt, and has aided the campaigns of numerous Illinois Republicans, including Gov. Jim Edgar and Labor Secretary and former Rep. Lynn Martin.

In recent months, he had criticized Dixon as a ''weather vane,'' who voted with President Bush when he was popular and then attacked him when he was not.

Williamson said he has raised $400,000 so far for the November campaign and has a $1 million commitment from the Republican Party`s Senate campaign fund.

His fundraising goal is $2 million for media advertising, and he said he needs $3.5 million overall ''to wage a race and win-$4.5 million would be even better.''

Because of Dixon`s conservatism, Republicans like Williamson have long been loath to criticize him. With Braun, all that could change. Al Hofeld`s media consultant David Axelrod described Braun as ''an affable, bright, articulate person who was able to project herself as being above the fray because the attack was being carried by another candidate.''

Axelrod predicted that Williamson`s stringent conservatism would be hard to sell to voters tired of years of Bush-Reagan policies.

Williamson, he suggested, would still have a tough fight in the fall.

''Candidates who represent business as usual and who were complicit in the Republican policies of the `80s and still defend them, I think, are vulnerable,'' he said.

''Rich Williamson not only helped implement the Reagan-Bush policies, he helped write them. He will have to defend them,'' Axelrod added. ''I don`t think people want to hear it in 1992.''